# what is principle of mathamatical induction    • -3
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive integers). It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.
The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion.
Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning.
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Principle of Mathematical Induction

If it is known that

(1) some statement is true for n = 1

(2) assumption that statement is true for n implies that the statement is true for
(n + 1)

then the statement is true for all positive integers
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